-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1041211644637425396389810245555', 'a10': [0.14231483827328514, -0.9898214418809327], 'a2': [0.41541501300188644, 0.9096319953545183], 'a3': [0.9594929736144974, -0.28173255684142967], 'a4': [-0.6548607339452851, 0.7557495743542583], 'a5': [-0.8412535328311812, -0.5406408174555976], 'a6': [0.6548607339452851, 0.7557495743542583], 'a7': [0.45535469155079195, 3.1670614450795456], 'a8': [-0.9594929736144974, -0.28173255684142967], 'a9': [0.8412535328311812, -0.5406408174555976], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 5.50967773946835, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-0.41541501300188644, -0.9096319953545183]]], [3, [[1.0, 0], [-0.9594929736144974, 0.28173255684142967]]], [5, [[1.0, 0], [0.8412535328311812, 0.5406408174555976]]], [23, [[1.0, 0], [4.793820311243345, 0.1388770085750758]]]], 'bad_primes': [2, 3, 5, 23], 'central_character': '690.211', 'coefficient_field': 'CDF', 'conductor': 690, 'conductor_radical': 690, 'conjugate': '2448226883284506186057501345242', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.41541501300188644, -0.9096319953545183]], [[1.0, 0], [-0.9594929736144974, 0.28173255684142967]], [[1.0, 0], [0.8412535328311812, 0.5406408174555976]], [[1.0, 0], [-0.45535469155079195, -3.1670614450795456], [-6.7164508153014815, 1.9721278978900079]], [[1.0, 0], [1.708130875482563, -3.740284890918972], [-7.2034680733981356, -8.313245317896842]], [[1.0, 0], [-0.4014591506095288, 2.7922097241156885], [-12.473408656988466, -3.662523238938586]], [[1.0, 0], [-5.331993383909932, -6.153448392107043], [-2.4193522506458476, 16.826964511975856]], [[1.0, 0], [1.5453628818413094, -1.783443837193055], [-2.7039819271924177, -18.80660739573772]], [[1.0, 0], [4.793820311243345, 0.1388770085750758]], [[1.0, 0], [-2.604600037585341, -3.0058686797560723], [-4.127130309925269, 28.70482181454705]], [[1.0, 0], [1.9024872342767818, 0.5586206544607043], [26.078859517766617, 16.759865341123525]], [[1.0, 0], [-1.510720009361843, 0.9708807974442323], [15.370355481069797, -33.65638382811718]], [[1.0, 0], [-2.6952494034416308, -1.7321316153281598], [17.03201553307734, 37.29491180953525]], [[1.0, 0], [-5.023876982800466, 1.4751433794134843], [36.17390191174079, -23.247555150590696]], [[1.0, 0], [6.435219622851782, 0], [47.0, 0]], [[1.0, 0], [-0.6553052345288987, -4.557748018291336], [-50.85312760156836, 14.931825512595774]], [[1.0, 0], [0.27747054562741347, -1.9298500345060028], [-56.61008544325534, -16.622220853644354]], [[1.0, 0], [-10.9636188047884, -3.2192089395631456], [51.31646550270205, 32.979089864791455]], [[1.0, 0], [2.0100746024762914, 4.4014494282459795], [-43.8756691743341, 50.63522148173531]], [[1.0, 0], [4.332198573510683, 9.486191662207997], [-46.49511211011524, 53.65821977915234]], [[1.0, 0], [-8.350760361116533, 9.63729119995693], [-10.388983193949816, -72.2569652573081]], [[1.0, 0], [-1.9221777810064018, 13.36904012140806], [-75.7999449155453, -22.256871990472945]], [[1.0, 0], [3.4305603021588973, -2.204687236020322], [34.479446079156574, -75.49945561442503]], [[1.0, 0], [10.250630266039272, -3.0098566154249884], [74.87156442197512, -48.11703275354819]], [[1.0, 0], [10.079192417516447, 6.477503648108753], [40.295256261182985, 88.23430354938829]], [[1.0, 0], [-14.162121860218697, 9.10144307346513], [41.956916313190526, -91.87283153080635]], [[1.0, 0], [-2.3276527395277022, 5.096848548271846], [-67.45065559636436, -77.84220615848861]], [[1.0, 0], [-4.938095053875465, -1.4499555324657478], [90.01412801293638, 57.84856746774894]], [[1.0, 0], [-5.648557993312451, -6.518783426581052], [-15.51231737178808, 107.89053716502167]], [[1.0, 0], [4.574559760731757, 10.016888636145705], [-73.99926293581721, 85.39970190203118]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 5, 'label': '2-690-23.4-c1-0-5', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/690/2/m/d/211/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [1.7581794464130616, 1.5394263749135366, 1.3124503077486713, 1.0698096657979734, 0.8046119257152234, 0.5124956931418604, 0.19309452758927445, -0.1491113914883101, -0.5045422920037064, -0.8588299957103834, -1.1936702017140293, -1.4881932578923414, -1.7208036524234092, -1.8713861621404766, -1.923710404831396, -1.8677996174246552, -1.7019783494620073, -1.4342909144881522, -1.082998924772775, -0.6759289606205447, -0.24855143708842395, 0.15917720776775932, 0.5069989294698835, 0.7591717912331697, 0.8893663535622957, 0.8849762938781166, 0.7501480364365019, 0.5069029529020992, 0.19390253350184833, -0.13731562317762117, -0.42845053854087795, -0.6223338143859956, -0.6716821416753119, -0.5475050150985733, -0.24583785101233735, 0.208465809706463, 0.7618725570169779, 1.336748463147671, 1.8402566020000783, 2.176743328271715, 2.262111968047785, 2.038163618147267, 1.4846289871276075, 0.6267036440408036, -0.46363557567303515, -1.6734416876245788, -2.8615774059474512, -3.877135839450638, -4.5810943087531735, -4.868002854075956, -4.684180898865382, -4.039141494003306, -3.007803331345648, -1.7224009110773577, -0.3546742246565009, 0.9093578392478114, 1.8982692233859466, 2.4830539999589614, 2.5990695705193683, 2.257971158279733, 1.547035295477254, 0.6153821506228835, -0.3510420321457587, -1.161698245447592, -1.6553333128216203, -1.7293464774438858, -1.3590410724747501, -0.602823470688672, 0.4080673007939103, 1.4937843529394672, 2.459756232336032, 3.1338718411655146, 3.399729303434375, 3.2192568548410723, 2.639950928559281, 1.7849753907837917, 0.8278518453414251, -0.04326866243821494, -0.6644333708722857, -0.9296434410556683, -0.8122438799031015, -0.3691500340778846, 0.27324932898878124, 0.9486489633783571, 1.489454447403869, 1.765877621465981, 1.716559062028844, 1.3634707538125528, 0.8072781219591213, 0.203779537810639, -0.27349851632929245, -0.47603803992022414, -0.31833337633471526, 0.1981195990266852, 0.9810978064519108, 1.865783368780581, 2.6511258573514005, 3.1462577662185085, 3.216052170438454, 2.814741127575776, 1.9990610871812629, 0.9171448166851518, -0.2247491334204547, -1.2100088281844217, -1.8624280893539373, -2.0873455662000935, -1.8926243440404904, -1.3837677503449324, -0.7339486249765874, -0.1362566145866316, 0.24965093148358297, 0.3424220809612288, 0.16307561123513242, -0.16899234565399354, -0.46807177950218287, -0.5347012547731521, -0.2152348417935948, 0.5476765119594432, 1.6881757484738613, 3.0227507936057574, 4.288826778812166, 5.20804842464959, 5.558714374573803, 5.2384146045117905, 4.299416755171788, 2.9456176698015817, 1.4894992567326473, 0.27809926390177103, -0.3942600349654239, -0.36428691303483623, 0.35188737836813144, 1.5543381691099516, 2.9021692079662667, 3.9944469455135745, 4.4698156967620815, 4.099753678737108, 2.851245225200835, 0.9018936651185615, -1.3975466535861127, -3.6046433769991193, -5.290551367865389, -6.142356638609936, -6.036283173082321, -5.0630390624670145, -3.4991455099992197, -1.7323822575235248, -0.16161065677557626, 0.9021435938300911, 1.3072070013303738, 1.0871513140159605, 0.43573022466167866, -0.3602407804946397, -1.0096218550053508, -1.3012995734414343, -1.1601312707602063, -0.6593801250849627, 0.012259681767001925, 0.6173814297220275, 0.9487725083877282, 0.8957003832264591, 0.4771220974669636, -0.1680136153079382, -0.8295699931340859, -1.2979104837746, -1.4349345718096058, -1.2210612445329059, -0.7623962052159138, -0.2551359129105327, 0.08174603412465997, 0.08378444464345447, -0.29734865942326943, -0.9691314288053924, -1.7202079449096455, -2.283906975554471, -2.4241683307219395, -2.016621124276668, -1.097965218096498, 0.13402719662384602, 1.372283744254349, 2.2896771195357197, 2.6387002266088277, 2.3300263403915897, 1.4639398873146068, 0.30279938601943457, -0.8087279588380273, -1.5517820524695038, -1.7358107710981645, -1.3620078576450179, -0.6256217229525143, 0.1459357522013997, 0.6014924460790948, 0.4874758238500809, -0.256967873505124, -1.463476534925827, -2.7714193495734687, -3.7300623153197194, -3.9364138003993467, -3.166560863422152, -1.4586903793766826, 0.8802763969063901, 3.349397122667845, 5.389362357395438, 6.5391051571375565, 6.565994159371566, 5.529675138015608, 3.759803443995718, 1.7545911337378184, 0.03182430785183167, -1.0211755876917779, -1.2521346889011955, -0.7713082521652778, 0.10475031839782296, 0.9726534075065308, 1.4841107994496752, 1.462772447795271, 0.9574013395796918, 0.21458448649838893, -0.4184576128671454, -0.6266521139066662, -0.2490044385919175, 0.6531168071087109, 1.8058673433944266, 2.808750933083659, 3.2679561143940528, 2.932123114062832, 1.784097510925186, 0.05674807287513597, -1.8335309073063684, -3.4141310017292885, -4.302184427109693, -4.320665349169571, -3.5463760200191587, -2.2748550797164375, -0.9155678857406119, 0.14572514794683514, 0.6699372139649654, 0.6314745902671097, 0.20782427313113633, -0.30162817395419883, -0.5961949608510917, -0.489146174851053, 0.02427719377220949, 0.7700318481275119, 1.4670136299298429, 1.8393521022561758, 1.726285592587949, 1.1476910912741256, 0.3000769379219005, -0.5158576095757643, -1.0088831005101426, -1.0088028076893063, -0.5327283735019942, 0.22050845112192205, 0.9472391890119046, 1.358957259990408, 1.2996800047988375, 0.8143913350134311], 'positive_zeros': ['0.821371160515337860463081977098039', '2.57467066943881102907481858181839', '3.57262881499687628580145265555258', '4.32199629315187596088941089112661', '5.44932134833782619879349772886708', '6.78332225240443220091481683097335', '7.70352036434726436169371850158349', '8.451938416549158402602243916230113', '9.618035835811879990560917691124352', '10.19951757082769197262097657642434'], 'prelabel': '2-690-23.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.3472702740563025, 'root_angle': -0.6191681271030646, 'root_number': '-0.3656934150823653 - 0.9307353684938576*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.309584063552', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.821371160515337860463081977098', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '2.57467066943881102907481858182', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.57262881499687628580145265555', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 5.50967773946835, 'bad_primes': [2, 3, 5, 23], 'central_character': '23.4', 'conductor': 690, 'conductor_radical': 690, 'degree': 2, 'index': 5, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/690/2/m/d/211/2'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': False, 'is_instance_G2Q': False, 'is_instance_HMF': False, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '2-690-23.4-c1-0-5', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-690-23.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.3472702740563025, 'root_angle': -0.3095840635515323, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.821371160515337860463081977098', 'prec': 107}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '1041211644637425396389810245555', 'Lhash_array': ['1041211644637425396389810245555'], 'label': '2-690-23.4-c1-0-5', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/690/2/m/d/211/2'}